{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:50Z","timestamp":1753893830151,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We relate the combinatorial definitions of the type $A_n$ and type $C_n$ Stanley symmetric functions, via a combinatorially defined \"double Stanley symmetric function,\" which gives the type $A$ case at $(\\mathbf{x},\\mathbf{0})$ and gives the type $C$ case at $(\\mathbf{x},\\mathbf{x})$.\u00a0 We induce a\u00a0 type $A$ bicrystal structure on the underlying combinatorial objects of this function which has previously been done in the type $A$ and type $C$ cases.\u00a0 Next we prove a few statements about the algebraic relationship of these three Stanley symmetric functions. We conclude with some conjectures about what happens when we generalize our constructions to type $C$.<\/jats:p>","DOI":"10.37236\/8872","type":"journal-article","created":{"date-parts":[[2020,7,28]],"date-time":"2020-07-28T12:55:41Z","timestamp":1595940941000},"source":"Crossref","is-referenced-by-count":0,"title":["Crystal Structures for Double Stanley Symmetric Functions"],"prefix":"10.37236","volume":"27","author":[{"given":"Graham","family":"Hawkes","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,7,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p15\/8133","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i3p15\/8133","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,7,28]],"date-time":"2020-07-28T12:55:57Z","timestamp":1595940957000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i3p15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,24]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,7,9]]}},"URL":"https:\/\/doi.org\/10.37236\/8872","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,7,24]]},"article-number":"P3.15"}}